Siemens AG, Europe’s largest engineering company, plans to cut as many as 1,600 jobs at its health-care division and will scale back the business after falling behind competitors including Roche Holding AG. The planned cuts amount to as much as 8 percent of workers at the diagnostics subsidiary, said Michael Sen, the chief financial officer of the health-care operations. Another 400 jobs will go as Siemens stops making linear accelerators that create radiation for cancer treatment. Chief Executive Officer Peter Loescher is embarking on the unit’s second major overhaul in less than two years, after Siemens spent more than 10 billion euros ($13 billion) since 2006 bolstering the diagnostics business. Order intake and sales at the health-care unit failed to grow in the most recent quarter, and profitability at the diagnostics business has slumped to less than half the rate two years earlier.